In designing mechanical part assemblies using computer aided design, manufacturing, and engineering (CAD/CAM/CAE) systems, it is useful to simulate and analyze the structural behavior of an assembly under operating conditions and the stresses experienced by the assembly under those operating conditions. Stress simulation and analysis operations are usually based on a geometrical discretization of the assembly using a finite element mesh representation of each part body in the assembly. Each mesh is usually comprised of nodes and elements interconnecting the nodes. These nodes and elements may take the form of solid elements such as tetrahedrons, hexahedrons, cubes, etc, surface elements such as triangles, quadrangles, and so-called 1-D elements such as bars and interconnecting links. Techniques for constructing such nodes and elements are described in, e.g., The Finite Element Method by O. C. Zienkiewicz and R. L. Taylor, McGraw Hill, 1989 [ref. 1], and The Finite Element Method by T. J. R. Hughes, Prentice-Hall, 1987 [ref. 2].
Existing stress analysis systems can work well with simple connections such as contact or fastened connections. However, more complex connections may not be dealt with in a fully satisfactory manner. One classical example of a complex connection is the tightening of a bolt in an assembly. The tightening of a bolt involves the application of a force, usually called a pre-tension force, that comes into play before other working loads. In some cases, CAD/CAM stress analysis systems ignore the complexity of such connections, or approximate them by treating them similarly to fastened connections. New systems and techniques for analyzing bolt and other pre-tensioned connections are to enable design engineers to better analyze assemblies of parts.